Explaining correlations by plotting orthogonal contrasts
Journal : American Statistician , vol. 60 , p. 335–339 , 2006
International Standard Numbers
Printed : 0003-1305
Electronic : 1537-2731
Publication type : Academic article
Issue : 4
DOI : doi.org/10.1198/000313006X1502...
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This article describes a new plot that aids understanding the relationship between two response variables in a designed experiment. In addition to plotting the observed values directly, we make a scatter plot of orthogonal contrasts from the general linear model. This plot contains the same correlation information as the ordinary scatter plot. Therefore, one can interpret how the effects of the various design variables contribute to the correlation coefficient. This idea is also useful in more general cases. Any graphic presentation of the original observations can be accompanied by a corresponding plot of orthogonal contrasts that often will clarify the interpretation.